I'm working on this problem and I'm having difficulty understanding the solution. In the solution, it states $a^3+b^3=(a+b)^3\rightarrow ab(a+b)=0$. What do these equations mean? It doesn't seem to fit the identity $a^3+b^3=(a+b)(a^2-ab+b^2)$ if the arrow meant subtracting.
I know that right arrows can define a function, but I don't see how $(a+b)^3\rightarrow ab(a+b)=0$ could be a function. If it is, then I don't know how it is applicable to the problem, in which case it would be great if someone could explain the rest of the solution.
P. S. I don't see this as asking two questions if that's not allowed. One is just a prerequisite to the other.